Stability estimate in the inverse scattering for a single quantum particle in an external short-range potential

TL;DR

This paper proves that the electric potential in a Schrödinger operator can be uniquely determined and stably reconstructed from scattering data in dimensions two and higher, advancing inverse quantum scattering theory.

Contribution

It establishes both uniqueness and Hölder stability estimates for recovering short-range electric potentials from scattering operators in higher dimensions.

Findings

Unique determination of the electric potential from scattering data.

Hölder stability estimate for the inverse problem.

Results valid for dimensions n ≥ 2.

Abstract

In this paper we consider the inverse scattering problem for the Schr{\"o}dinger operator with short-range electric potential. We prove in dimension n $\geq$ 2 that the knowledge of the scattering operator determines the electric potential and we establish H{\"o}lder-type stability in determining the short range electric potential.